The security on one's credit data is considerably tighter than that of one's government records. Of course, there are still rare incidents where a person's credit information will be in error. And its a pain to correct but it can be fixed. Of greater concern is that a person's credit information can be stolen (identity theft is a chief cause of this, and this falls on the government). Any ID system ought to be as close to impossible to breach as is humanly possible.
We also have to realize that the government, being composed of people, is no more or less trustworthy than any other person or entity including the likes of Bill Gates, General Electric, or the average joe on the street corner. I have a tendency to not trust any of these entities 100%. In fact, there are but a handful of people that I do trust. They are my true friends. Others must earn it.